Question and Answers Forum

All Questions      Topic List

Others Questions

Previous in All Question      Next in All Question      

Previous in Others      Next in Others      

Question Number 51250 by Tawa1 last updated on 25/Dec/18

Given that z_1 = R_1 + R + jωL ; z_2 = R_2 ; z_3 = (1/(jωC_3 )) and z_4 = R_4 + (1/(jωC_4 )) and also that z_1 z_3 = z_2 z_4 , express R and L in terms of the real constants R_1 , R_2 , R_4 , C_3 and C_4 Answer: R = ((R_2 C_3 − R_1 C_4 )/C_4 ) , L = R_2 R_4 C_3

$$\mathrm{Given}\:\mathrm{that}\:\:\:\mathrm{z}_{\mathrm{1}} \:=\:\mathrm{R}_{\mathrm{1}} \:+\:\mathrm{R}\:+\:\mathrm{j}\omega\mathrm{L}\:;\:\:\:\mathrm{z}_{\mathrm{2}} \:=\:\mathrm{R}_{\mathrm{2}} \:;\:\:\mathrm{z}_{\mathrm{3}} \:=\:\frac{\mathrm{1}}{\mathrm{j}\omega\mathrm{C}_{\mathrm{3}} } \\ $$$$\mathrm{and}\:\:\mathrm{z}_{\mathrm{4}} \:=\:\mathrm{R}_{\mathrm{4}} \:+\:\frac{\mathrm{1}}{\mathrm{j}\omega\mathrm{C}_{\mathrm{4}} }\:\:\mathrm{and}\:\mathrm{also}\:\mathrm{that}\:\:\:\mathrm{z}_{\mathrm{1}} \mathrm{z}_{\mathrm{3}} \:\:=\:\:\mathrm{z}_{\mathrm{2}} \mathrm{z}_{\mathrm{4}} \:,\:\:\:\mathrm{express}\: \\ $$$$\mathrm{R}\:\mathrm{and}\:\mathrm{L}\:\mathrm{in}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{the}\:\mathrm{real}\:\mathrm{constants}\:\:\mathrm{R}_{\mathrm{1}} ,\:\mathrm{R}_{\mathrm{2}} ,\:\mathrm{R}_{\mathrm{4}} ,\:\mathrm{C}_{\mathrm{3}} \:\mathrm{and}\:\mathrm{C}_{\mathrm{4}} \\ $$$$ \\ $$$$\mathrm{Answer}:\:\:\:\:\:\:\mathrm{R}\:=\:\frac{\mathrm{R}_{\mathrm{2}} \mathrm{C}_{\mathrm{3}} \:−\:\mathrm{R}_{\mathrm{1}} \mathrm{C}_{\mathrm{4}} }{\mathrm{C}_{\mathrm{4}} }\:,\:\:\:\:\:\:\:\:\mathrm{L}\:=\:\mathrm{R}_{\mathrm{2}} \mathrm{R}_{\mathrm{4}} \mathrm{C}_{\mathrm{3}} \\ $$

Answered by tanmay.chaudhury50@gmail.com last updated on 25/Dec/18

z_1 z_3 =z_2 z_4 (R_1 +R+jwL)(1/(jwC_3 ))=R_2 (R_4 +(1/(jwC_4 ))) comparing real and imaginary part ((R_1 +R)/(jwC_3 ))=(R_2 /(jwC_4 )) R_(1 ) C_4 +RC_4 =R_2 C_3 R=((R_2 C_3 −R_1 C_4 )/C_4 ) (L/C_3 )=R_2 R_4 [L=C_3 R_2 R_4

$${z}_{\mathrm{1}} {z}_{\mathrm{3}} ={z}_{\mathrm{2}} {z}_{\mathrm{4}} \\ $$$$\left({R}_{\mathrm{1}} +{R}+{jwL}\right)\frac{\mathrm{1}}{{jwC}_{\mathrm{3}} }={R}_{\mathrm{2}} \left({R}_{\mathrm{4}} +\frac{\mathrm{1}}{{jwC}_{\mathrm{4}} }\right) \\ $$$${comparing}\:{real}\:{and}\:{imaginary}\:{part} \\ $$$$\frac{{R}_{\mathrm{1}} +{R}}{{jwC}_{\mathrm{3}} }=\frac{{R}_{\mathrm{2}} }{{jwC}_{\mathrm{4}} } \\ $$$${R}_{\mathrm{1}\:} {C}_{\mathrm{4}} +{RC}_{\mathrm{4}} ={R}_{\mathrm{2}} {C}_{\mathrm{3}} \\ $$$${R}=\frac{{R}_{\mathrm{2}} {C}_{\mathrm{3}} −{R}_{\mathrm{1}} {C}_{\mathrm{4}} }{{C}_{\mathrm{4}} } \\ $$$$\frac{{L}}{{C}_{\mathrm{3}} }={R}_{\mathrm{2}} {R}_{\mathrm{4}} \:\:\:\:\left[{L}={C}_{\mathrm{3}} {R}_{\mathrm{2}} {R}_{\mathrm{4}} \right. \\ $$$$ \\ $$

Commented by Tawa1 last updated on 25/Dec/18

God bless you sir

$$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir} \\ $$

Commented by tanmay.chaudhury50@gmail.com last updated on 26/Dec/18

thank you...

$${thank}\:{you}... \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com